Though not everybody who liked their health plan could keep it as President Obama once famously said, there were still just a small percentage of Americans who had their policies cancelled last year despite some overhyped predictions.

About 2.2 percent of Americans who purchased coverage on their own, or 400,000 people, had individual policies cancelled, according a new analysis from the nonpartisan Urban Institute. And just 0.3 percent of Americans with coverage through their employer, or 500,000 people, had their health insurance policies cancelled in 2014, the Institute said. Authors of the issue brief, funded by the Robert Wood Johnson Foundation, said there was no evidence of a significant number of policy cancellations in either the self-insured or small group markets.

“Plan cancellations of policies that do not meet Affordable Care Act standards were kept to a minimum in 2014,” Kathy Hempstead, who directs coverage issues at the Robert Wood Johnson Foundation, said in a statement companying the report.

Policies were generally cancelled because these plans didn’t comply with the Affordable Care Act’s requirements that health plans sold on government exchanges have 10 essential health benefits. Plans also had to comply with other consumer protections such as “prohibiting preexisting condition exclusions and premiums based on health status or sex.”

Though there were many reports that millions received cancellation notices, government policy changes blunted the impact of people actually having their policy cancelled. But numerous changes in government policy blunted the impact of cancellations.

Going forward Hempstead doesn’t see cancellations being a big issue.

“I would expect them to taper off slowly,” Hempstead said. “It suggests plan cancellations are much less of an issue now than they were in 2013. I think consumers were caught by surprise during the first wave of cancellations but insurers were basically expecting it.”

Insurance companies have said they have recouped a lot of the cancelled business or mitigated their losses. Most insurers such as Anthem (ANTM), Aetna AET +1.93% (AET) and UnitedHealth Group UNH +0.32% (UNH) have expanded their health insurance offerings giving Americans who take to the exchanges more choices.

The market, though, could continue to shake out to the detriment of smaller carriers.